454 | Energy Environ. Sci., 2016, 9, 454--460 This journal is©The Royal Society of Chemistry 2016

Cite this: Energy Environ. Sci.,

2016, 9, 454

Broad temperature plateau for high ZTs in heavilydoped p-type SnSe single crystals†

Kunling Peng,ab Xu Lu,a Heng Zhan,a Si Hui,c Xiaodan Tang,ab Guiwen Wang,ab

Jiyan Dai,d Ctirad Uher,c Guoyu Wang*b and Xiaoyuan Zhou*a

Excellent thermoelectric performance is obtained over a broad

temperature range from 300 K to 800 K by doping single crystals

of SnSe. The average value of the figure of merit ZT, of more than

1.17, is measured from 300 K to 800 K along the crystallographic

b-axis of 3 at% Na-doped SnSe, with the maximum ZT reaching a

value of 2 at 800 K. The room temperature value of the power factor

for the same sample and in the same direction is 2.8 mW mK�2,

which is an order of magnitude higher than that of the undoped

crystal. Calculations show that Na doping lowers the Fermi level

and increases the number of carrier pockets in SnSe, leading to a

collaborative optimization of the Seebeck coefficient and the elec-

trical conductivity. The resultant optimized carrier concentration

and the increased number of carrier pockets near the Fermi level in

Na-doped samples are believed to be the key factors behind the

spectacular enhancement of the average ZT.

1. Introduction

To satisfy energy demands in a modern society, the focus hasshifted towards utilizing green technologies and alternativeenergy sources to reduce the dependence on fossil fuels. Thermo-electric (TE) devices, which can serve as heat pumps or recoverwaste heat to generate electrical power, are promising candi-dates.1,2 The efficiency of a thermoelectric material is determinedby the dimensionless figure of merit ZT, defined as ZT = S2sT/k,where S is the Seebeck coefficient, s is the electrical conductivity,S2s is the power factor (PF) and k is the thermal conductivity

consisting of the lattice conductivity (kl) and the electronicconductivity (ke). To achieve high ZT, several general strategieshave emerged in the past two decades. One such strategy isband engineering, which is implemented by the convergenceof electronic bands,3,4 distortions in the electronic density ofstates (DOS),5 and alignments of the valence or conductionbands.6 Another strategy is structural engineering that includesdesigning new compounds with complex crystal structures7,8,introducing nanostructures and developing lower-dimensionalmaterials.9 Such approaches are typically used with thepolycrystalline thermoelectric materials. In contrast, singlecrystals are rarely used as thermoelectric materials primarilybecause they are fragile, often cleave easily, and due to theabsence of grain boundaries, single crystals possess high thermalconductivity.

Currently, exploring the thermoelectric properties of twobulk single-crystalline structures: SnSe10,11 and In4Se3,12 both ofwhich are actually quasi-laminar structures is gaining consider-able interest.

a College of Physics, Chongqing University, Chongqing 401331,

People’s Republic of China. E-mail: xiaoyuan2013@cqu.edu.cnb Chongqing Institute of Green and Intelligent Technology,

Chinese Academy of Sciences, Chongqing 400714, People’s Republic of China.

E-mail: guoyuw@cigit.ac.cnc Department of Physics, University of Michigan, Ann Arbor, MI 48109, USAd Department of Applied Physics, The Hong Kong Polytechnic University, Kowloon,

Hong Kong, China

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c5ee03366g

Received 4th November 2015,Accepted 2nd December 2015

DOI: 10.1039/c5ee03366g

www.rsc.org/ees

Broader contextMost of the enhancements in ZT in the past decade have been accom-plished by reducing the thermal conductivity because it has provenexceedingly difficult to enhance the power factor. Zhao et al. reportedthat pure single crystals of SnSe are very promising thermoelectricmaterials with an intrinsic ultralow thermal conductivity and a record-high maximum ZTmax of 2.6 along the b-axis at 923 K; however, an averageZTave for pure SnSe is only 0.23 in this temperature range. In this study,we report a high average ZTave of B1.2 achieved in p-type SnSe singlecrystals doped with Na from 300 K to 800 K. The peak ZTmax value inexcess of 2.0 was reached at 800 K. We found that SnSe is a uniquematerial where more than three electronic bands contribute to the chargetransport and hence, to the power factor. By heavy p-type doping, weaccess lower lying valence bands, the contribution of which dramaticallyenhances the electrical conductivity, while the Seebeck coefficient ismaintained at reasonably large values. Our study provides a new directionfor investigating different types of earth-abundant, low-cost and environ-mentally friendly anisotropic single crystals for thermoelectric energyconversion applications at low and moderate temperatures.

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SnSe is a compound consisting of earth-abundant and environ-mentally friendly elements and has recently been shown to have anultrahigh thermoelectric performance with the maximum ZTof 2.6 reached at 923 K along the b-axis.10 However, this excep-tionally high peak value of ZT is found in the high-temperaturephase of SnSe (T 4 800 K, Cmcm space group #63, a = 4.31 Å,b = 11.70 Å, c = 4.31 Å),13 while the thermoelectric performance ofthe low-temperature phase (T o 800 K, Pnma space group #62,a = 11.49 Å, b = 4.44 Å, c = 4.135 Å) is rather poor, which greatlylimits applications of this material.

In this study, we demonstrate an excellent thermoelectricperformance achieved in doped Sn(Na, Ag)Se single crystalsover a broad range of temperatures with the average ZT valuewell in excess of unity from room temperature to 800 K, whereinthe maximum ZT attains values of 2 or better. Our study focuseson the performance along the b direction in SnSe, wherein thebest results have been reported previously. For comparison, theaverage ZT we obtain in a single crystal of Sn97Na3Se100 alongthe b-axis is greatly enhanced and is about 1.5 times larger thanthat of the undoped SnSe crystal in the same direction. Basedon our theoretical estimates and the experimental data, we findthat the Fermi level can be shifted to the desired range of energiesby doping with Na or Ag. This greatly improves the overall thermo-electric performance and makes SnSe single crystals useful over avery wide range of temperatures.

2. Experimental and theoreticalmethods2.1. Synthesis

Elemental constituents were weighed according to the stoichio-metry of Sn1�xRxSe (R = Na, Ag; x = 0, 1, 2, 3) and loaded intoquartz tubes under an argon atmosphere and sealed at 5� 10�4 Pa.The quartz tubes were heated up to 1273 K over 12 h, kept atthat temperature for 10 h, and subsequently furnace cooled toroom temperature. The obtained ingots (B15 g) were crushedinto a powder and sealed again in a cone-shaped quartz tubeunder argon. Single crystals were grown by a modified Bridgmanmethod. The presence of argon gas during the growth protectsthe crystal from oxidation because the cone-shaped quartz tubesoften break as the structure undergoes a phase transition fromthe Cmcm to the Pnma phase. Excellent single crystalline ingotsof Sn1�xRxSe with diameter of 13 mm and height of 15 mmwere obtained.

2.2. Measurements

The obtained single crystal ingots were cut into B9 mm �3 mm� 2 mm rectangular-shaped samples for electrical propertymeasurements and square planar samples of B6 mm � 6 mm�1.5 mm for thermal conductivity measurements. Electricalconductivity and the Seebeck coefficient were measured usinga LSR-3 (Linseis, Germany) instrument under a static heliumatmosphere. Thermal diffusivity (D) was obtained on a LFA 457(Netzsch, Germany) instrument, and the specific heat capacitywas used as suggested by ref. 10, which is comparable to the

reported values.14 The thermal conductivity was calculatedusing k = rDCp, where r is the density. The combined uncer-tainly for all measurements involved in the calculation of ZT isaround 15%. The lattice thermal conductivity was obtained bysubtracting the electronic thermal conductivity ke from thetotal thermal conductivity, kl = k � ke, using the Wiedemann–Franz law, ke = sLT, where L is the Lorenz constant. Due to thecomplexity and the non-parabolicity of the valence band struc-ture around the Fermi level for p-type SnSe, accurate determi-nation of the L is difficult. An estimation of L was made using asingle parabolic band (SPB) model with acoustic phonon scat-tering, resulting in an L with a deviation of less than 10% ascompared with a more rigorous single non-parabolic band andmultiple band models calculation.15,16 Irrespective of the valueemployed for the Lorenz constant, the total thermal conducti-vity, the final ZT, and the conclusion in this study were notaffected.

The temperature-dependent Hall coefficient was measuredusing 16 Hz low-frequency excitations with a Linear ResearchAC Resistance Bridge (LR-700) in the applied field of �1 Tgenerated by an air-bore Oxford superconducting magnetaccommodating a tubular oven with a Hall-probe insert. Crystalstructures were determined using an X-ray single crystal diffracto-meter (SuperNova, Agilent) and transmission electron microscopystudies were carried out using a JEOL 2100F microscope.

2.3. Density function theory (DFT) calculations

The projector augmented plane wave (PAW) method17,18 asimplemented in the Vienna ab initio simulation package (VASP)19

code was used for structural relaxation. The exchange–correlationfunctional was defined using a generalized gradient approxi-mation (GGA) of Perdew–Burke–Ernzerhof (PBE).20 Super cells(2 � 2 � 2, Pnma) with 64 atoms were built for the purpose ofrandomly replacing Sn atoms with Na or Ag atoms corres-ponding to the doping amount of B3 percent. The cut-off energyin the plane wave expansion was set at 500 eV. The atomicpositions were relaxed until the forces on the atoms were smallerthan 0.01 eV Å�1. For the Brillouin zone integrations, we usedthe Monkhorst–Pack k-mesh scheme with 3 � 5 � 5 for Pnmawhen calculating the total energy and 7� 13� 13 for Pnma whencalculating the DOS. Another super cell (1 � 5 � 5, Pnma) with200 atoms was built to calculate the Fermi level for Sn1�xNaxSe(x = 0, 0.01, 0.02, 0.03, 0.04) without relaxing the super cell butthe primitive cell in the Pnma structure.

3. Results and discussion3.1. Crystal structure characterization

To confirm that the obtained samples are single crystals, XRDanalysis and transmission electron microscopy (TEM) werecarried out. Fig. 1 shows nice single crystal cleavage faces alongthe b–c plane (Fig. 1a, inset 1), an electron diffraction pattern(Fig. 1a, inset 2), a high-resolution TEM image (Fig. 1a, inset 3),and the interpretation of the XRD single crystal diffraction data(Fig. 1b). The high-resolution TEM image of the single crystal

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Sn0.97Na0.03Se shows a well-organized crystal lattice and unitcells projected along the [100] direction can be identified, whilethe electron diffraction pattern along the [100] direction canbe readily indexed to the SnSe structure at room temperature.The crystal structure of SnSe based on the single crystal diffrac-tion data is shown in Fig. 1b and confirms that the structurebelongs to the Pnma space group (a = 11.493 Å, b = 4.152 Å,c = 4.438 Å).

3.2. Electronic structure calculations

Calculated Fermi levels for the crystals doped with 1%, 2%, 3%,and 4% of Na are shown in Fig. 2a. It is apparent that the Fermilevel is lowered when the content of Na increases, and the topof the valance band remains at around 3.5 eV; the result isdepicted by the blue solid line in Fig. 2b, where the top bandsrefer to VB1 or VB2 and the sub-bands refer to VB3 or VB4(see also Fig. 3).

The first row of panels in Fig. 3 indicates that the DOS nearthe Fermi level is derived from the s- and p-orbitals of Sn andespecially from the p-orbitals of Se. The contribution of thedoping elements Na and Ag to the DOS is almost negligible.However, the doping elements change the profile of the originalDOS by increasing the number of carrier pockets near theFermi level (see also Fig. 2b). As is well known, the increasein the local DOS near the Fermi level can greatly enhance the

Seebeck coefficient, which for a degenerate system is given bythe Mott expression21

S ¼ p2

3

kB2T

q

dnðEÞndE

þ dmðEÞmdE

� �E¼EF

(1)

with

n[E] = g[E] f[E] (2)

where kB is the Boltzmann constant, f (E) is the Fermi function,q is the carrier charge, n(E) is the carrier concentration, m(E) isthe carrier mobility, and g(E) is the density of states (DOS).Thus, the Seebeck coefficient S depends on the energy deriva-tive of the density of states, which increases via doping com-pared to that of the undoped sample.5 Based on the total DOSanalysis, we can also qualitatively understand that the carrierconcentration ( p(E)) depends on the energy derivative of theenergy-dependent DOS, which largely increases via dopingcompared to that of the undoped sample, yielding an increasein the carrier concentration as well as in the electrical con-ductivity as the Na and Ag doping contents increase, as shownin Fig. 4b and a, respectively.

Doping modifies the band structure of the Pnma phase ofSnSe in two major ways: it shifts the position of the Fermi leveland it tends to flatten the top of the valence band; both effectsare illustrated in Fig. 3. The shift of the Fermi level upon

Fig. 1 The crystal structure of SnSe. (a) High-resolution TEM images of a single crystal of Sn0.97Na0.03Se and the electron diffraction pattern along the[100] direction (inset) at room temperature; (b) the Pnma structure based on the single crystal diffraction data of Sn0.97Na0.03Se.

Fig. 2 Density of states in the Pnma phase of SnSe. (a) The total DOS of Sn1�xNaxSe (x = 0, 0.01, 0.02, 0.03, 0.04) in the Pnma structure. The valanceband edge is at 3.5 � 0.05 eV for all samples in calculations; (b) the Fermi level as a function of doping concentration and temperature in the Pnmastructure. The blue line shows the Fermi level as a function of Na doping concentration, which can also apply qualitatively to other dopants in SnSe.(The top bands refer to VB1 or VB2; the sub-bands refer to VB3 or VB4, see also Fig. 3).

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doping is significant and for a high enough doping content(such as 3% of Ag or Na), the Fermi level enters the valence band,turning the structure into a metal. At the same time, the flattenedvalence band edge upon doping, especially when Na is used, givesrise (via eqn (3)) to an enhanced effective mass and thus Na andAg doping increases the band effective mass of holes.

1

�h2@2E

@k2

� �k¼ki¼ 1

m�(3)

In eqn (3), �h is the Planck constant and ki is the wave vector ofthe i-th carrier pocket. Moreover, the band gap slightly narrowsupon doping. It can be noted that in sufficiently doped samples,in addition to the carrier pockets at the top of the valence band(e.g. VB1, VB2 in Fig. 3), the carrier pockets of the lower lyingvalence bands (e.g. VB3, VB4 in Fig. 3) may also contribute tothe electronic transport.22,23

As discussed in the literature,1,22 the increase in carrierpockets near the Fermi level (when multiple bands have the

Fig. 3 Electronic band structure and DOS for the Pnma structure with the super cell.

Fig. 4 Temperature dependence of electronic transport properties. (a) Electrical conductivity; (b) inverse RH of Sn0.99Na0.01Se and Sn0.98Na0.02Se thatgive an indication of the carrier concentration and inset is the carrier concentration of PbTe-Tl5 and Mg2Si0.3Sn0.7;24 (c) the Fermi level as a function oftemperature in the Pnma structure illustrated by the red line. The heavy bands refer to VB1 or VB2; the light bands refer to VB3 or VB4 (see Fig. 3);(d) Seebeck coefficient; (e) the Pisarenko relation given by the red solid line (Seebeck coefficient vs. carrier concentration) assuming a single parabolicband model at room temperature compared to the estimated results measured on all Sn1�xRxSe samples (blue dot or green fitting line) of this study. Thedifference between the red line and the green line indicates that the single band model is not adequate for this material; (f) the power factor.

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same or comparable energy within a few kBT) can enhance theSeebeck coefficient. Herein, we list some differences in theband energy (see Fig. 3): DE(VB1–VB2) = 0.020 eV, DE(VB4–VB3) =0.038 eV for the pure sample; DE(VB2–VB1) = 0.017 eV,DE(VB4–VB3) = 0.028 eV for Sn0.97Ag0.03Se; DE(VB2–VB1) =0.011 eV, DE(VB4–VB3) = 0.022 eV for Sn0.97Na0.03Se. Further-more, theoretical calculations show that the number of carrierpockets in sub-bands is 6, indicating that a high multiplecarrier pocket is achieved near the Fermi level through dopingand the Seebeck coefficient should be enhanced.

3.3. Electronic transport properties

Temperature dependence of the electrical conductivity (s), thecarrier concentration, the Seebeck coefficient, and the powerfactor are presented in Fig. 4. The electrical conductivity inFig. 4a shows two distinct regions of conduction. At low tem-peratures, the electrical conductivity shows a metallic characterwith the conductivity decreasing as the temperature increases.At high temperatures, thermal activation of charge carrierstakes place and the electrical conductivity increases with increas-ing temperature. The cross over between the two regimes ofconduction depends on the degree of doping. One can also seethat the electrical conductivity of the Na and Ag doped singlecrystals is at least an order of magnitude higher than theconductivity of the pure SnSe crystals. It should be noted thatall Na-doped samples show at least 50 times higher electricalconductivity at room temperature than the undoped crystals.As shown in Fig. 2b, the inverse RH of Sn0.99Na0.01Se andSn0.98Na0.02Se (Fig. 4b) are indeed high, which naturallyindicates the high electrical conductivity in Na-doped samples.More importantly, besides the contribution from the increasedcarrier concentration, the high electrical conductivity benefitsfrom the higher total DOS near the Fermi level, as discussed inrelation to Fig. 2 and 3. It can also be noted from Fig. 4 that theelectrical conductivity of the Na-doped crystal is much higherthan that of the Ag-doped crystal at the same doping level. Thiswe attribute to the different valence states of the two dopantsand their effects on electron scattering.

Because all doped single crystals in the low temperature regionshow a linear relationship between the logarithm of conductivity(base 10) and temperature, rather than the conductivity fallingapproximately inversely with the temperature as in case of metals,this implies that the carrier concentration decreases as thetemperature increases. This is indeed confirmed by Hall effectmeasurements shown in Fig. 4b where the carrier densities ofSn0.99Na0.01Se and Sn0.98Na0.02Se crystals decrease rapidly with therising temperature; this trend is distinctly different from thatobserved in other popular TE materials (see Fig. 4b, inset5,24).The decrease in the carrier concentration means that the DOSdecreases. Eventually, at elevated temperatures, an activated(semiconducting) behavior sets in. We believe that the Fermilevel shifts with the temperature and the red line in Fig. 4cschematically indicates this trend.

Fig. 4d shows the Seebeck coefficient of all samples. Dopedsingle crystals have a rather small Seebeck coefficient andNa-doped crystals have a smaller Seebeck coefficient than that

of Ag-doped crystals of comparable doping content. We alsonote that the Seebeck coefficient of Sn0.99Na0.01Se is larger thanthat of Sn0.98Na0.02Se and Sn0.97Na0.03Se, the latter two crystalshaving comparable values. Nevertheless, all doped SnSe crystals,regardless of whether Ag or Na doped, lie well above the Pisarenkoline in Fig. 4e. We attribute this to the beneficial effect of multiplecarrier pockets in the doped SnSe crystals. In addition, thedeviation from the Pisarenko line25 indicates that the single bandmodel is not adequate for this material and the multi-band modelis necessary for accurate theoretical fitting. Although the Seebeckcoefficient of Na-doped crystals is distinctly smaller than theSeebeck coefficient of Ag-doped crystals (see Fig. 4d and e), themuch higher electrical conductivity of the former yields muchlarger power factors compared to the Ag-doped SnSe crystals. Thisis illustrated by Fig. 4f, where the power factor of all crystals isplotted against the temperature. The highest Na-doped crystal,Sn0.97Na0.03Se, shows excellent electronic properties with thepower factor of more than 1.38 mW mK�2 in the whole tempera-ture range and the power factor as high as 2.8 mW mK�2 at roomtemperature. Compared to other thermoelectric materials, thepower factor achieved in the Sn0.97Na0.03Se crystal is quite highand competes very favorably with efficient thermoelectric materi-als such as PbTe,26 Mg2Si1�xSnx,24,27 FexCo1�xSb3,28 and Bi3Te4.29

Based on the previous discussion, we attribute the large enhance-ment in the power factor of Sn0.97Na0.03Se to the presence ofmultiple carrier pockets and the lowered Fermi level.

3.4. Thermal transport properties

The temperature dependence of the total thermal conductivity(k) for all samples is shown in Fig. 5a. The total thermalconductivity of all samples is in the range between 1.78 and2.24 W mK�1 at room temperature, confirming the result fromprevious studies (around 1.8 W mK�1).11 The lattice thermalconductivity (kl) is calculated by subtracting the electronic partfrom the total thermal conductivity, as shown in Fig. 5b. Thevalues of kl are quite low and are similar to polycrystalline samplesof other important families of thermoelectric materials such asPbTe26, Mg2Si1-xSnx,24,27 FexCo1�xSb3.28 The lattice thermal con-ductivity follows approximately the 1/T temperature dependencecharacteristic of the dominance of Umklapp phonon processes.30

Apparently, a strong bonding anharmonicity10 contributes to suchlow lattice thermal conductivities. Ag-doping shows little effect onthe lattice thermal conductivity. This is understandable in view ofthe similar size and mass of Ag and Sn atoms, and therefore has aminimal effect on the scattering of phonons. A very differentsituation arises in the case of Na-doped SnSe where Na and Snhave very different sizes and masses (inset in Fig. 5b) and thus themass-and size-dependent scattering of phonons is significant. Thisis clearly seen in Fig. 5b, wherein with the increasing content ofNa, the lattice thermal conductivity decreases quite markedly.

3.5. Overall figure of merit

The figure of merit was calculated based on the experimentaldata of the relevant transport parameters. As compared to theundoped sample reported by Zhao et al., which previouslyprovided the record-high ZT values,10 Na-doped SnSe crystals

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possess a higher figure of merit, especially the heaviest dopedSn0.97Na0.03Se. This undoped SnSe exceed the figure of merit ofthe Sn0.97Na0.03Se crystal only at temperatures above 800 K. Theperformance of Na-doped single crystals is also much better thanthat of Ag-doped SnSe. The difference in the performance derivesmainly from the superior electronic properties of Na-doped crys-tals. Over the temperature range from 300 K to 800 K, the averageZT value of 1.17 is obtained for the Sn0.97Na0.03Se crystal, which isindeed an excellent and highly competitive value compared to thebest results of currently explored TE materials.10,26,31–38 All theabovementioned results show that Sn0.97Na0.03Se is a very promis-ing TE material over a broad range of temperatures, with a goodthermal stability (see Fig. S5, ESI†). As the previous studies haveshown, SnSe can be used at temperatures approaching 950 K andthus, even higher average values over a broader range of tempera-tures are likely (Fig. 6).

4. Conclusions and outlook

Combining theoretical calculations with experimental studies,we explored the effect of doping SnSe single crystals with twodistinct elements, Na and Ag. Calculations show that the Fermilevel is shifted upon doping, the valence band edge is flattened,and the number of carrier pockets is enlarged. All three effectshave a positive influence on the electronic transport and thermo-electric properties of doped SnSe along the b-axis, the directionwhere the performance is maximized. Moreover, the significantlydifferent mass and size of Na atoms compared to atoms of Sngive rise to a strong mass and size defect scattering of phonons,

which reduces the lattice thermal conductivity quite markedly.The overall effect is an excellent power factor and figure of merit,which extend over a broad range of temperatures. This is seenparticularly in the case of Sn0.97Na0.03Se wherein the average ZTvalue over the temperature range from 300 K to 800 K reacheswell over unity, and the figure of merit at 800 K is in excess of 2.Coupled with their non-toxic nature and the fact that theypresent no major environmental concerns, the doped SnSecrystals offer excellent thermoelectric performance over a verybroad range of temperatures.

Acknowledgements

The study is financially supported in part by the National NaturalScience Foundation of China (Grant no. 11344010, 11404044,51472036) and the Fundamental Research Funds for the CentralUniversities (CQDXWL-2013-Z010). The study at the ChongqingInstitute of Green and Intelligent Technology, Chinese Academyof Sciences is supported by the One Hundred Person Project of theChinese Academy of Science, Grant No. 2013-46. CU. HS acknowl-edges the support from CERC-CVC, the joint US-China Programsupported by the U.S. Department of Energy, under the AwardNumber DE-PI0000012.

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Fig. 6 Figure of merit. (a) Figure of merit in this study; (b) ZT values for several popular TE materials with the red numbers indicating the average ZT valuesranging from 300 to 800 K for each material (for MgAgSb the range is from 300 to 550 K). Clearly, doped SnSe single crystals are very promising.

Fig. 5 The thermal properties as a function of temperature. (a) Thermal conductivity. (b) Lattice thermal conductivity and inset is schematic diagram ofdifference between Ag and Na.

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